Interest
This is compound interest.
What is earning interest on interest?
This is the difference between exponential growth and decay.
What is growth increases and decay decreases?
This is how a logarithm relates to an exponent.
What is they are inverses?
This is any change made to a parent function, such as y=log10(x).
What is a transformation?
This is the base for continuous interest.
What is the number e?
This is an example of exponential growth (except interest).
(Answers vary)
This is the special log with a base of 10.
What is the common log?
This is the parent function for exponential growth.
What is f(x) = 10x?
This is what happens to the total interest as the number of compounding steps increases.
What is the interest increases, with diminishing returns?
A famine is sweeping across a country, killing 1% of the population every year, compounded monthly. This is an example of (growth or decay?).
What is compound decay?
This is the special log with a base of e.
What is the natural log?
This is the imaginary line that some graphs, like exponents and logarithms, approach but never quite reach.
What is an asymptote?
The population of Bixby is about 30,000 and is growing at a rate of about 3% continuously. Assuming this trend continues, this will be the population of Bixby in the year 3000, and this is why this number is realistic or not.
What is 1.5 * 1017, and not realistic because it is far too large?
$0.93 at 2.25% annual interest for a term of 1000 years yields this much interest.
What is $4.3B?
This is an example of exponential decay.
(Answers vary)
**DAILY DOUBLE**
This is 14x+1 = 120 rewritten as a logarithm.
What is log14(120) = x+1?
These are the transformations applied to 3log(2x) + 4.
What are a vertical shift up 4, a vertical stretch by a factor of 3, and a horizontal stretch by a factor of 2?
Mr. Landin deposits $7,500 into his Roth IRA at an average return of 8% continuously. This is how much money he has in 36 years when he's ready to retire.
What is $133607?
A pie is cooling on a windowsill. It starts at a temperature of 98 degrees Celsius and cools at a rate of 12% per minute. What will the temperature of the pie be after 15 minutes, assuming continuous decay?
What is 16.19 degrees Celsius?
This is log7(14) rewritten as a common log, using the change of base property.
What is log(14)/log(7)?
These are the transformations applied to f(x) = 103x+2 - 5
What is a vertical shift down 5, a horizontal shift left 2, and a horizontal stretch by a factor of 3?